Multiple choice

The ratio of the curved surface area to the total surface area of a cylinder is 3 : 5. Find out the volume of the cylinder if the curved surface is 462 cm2. (π = 22/7) एक सिलेंडर के वक्रपृष्ठ क्षेत्रफल तथा सम्पूर्णपृष्ठ क्षेत्रफल का अनुपात 3:5 है। तो बेलन का आयतन ज्ञात कीजिये यदि वक्रपृष्ठ क्षेत्रफल 462 सेमी2 है। (π = 22/7)

  1. 1228

  2. 1723

  3. 1540

  4. 1617

  5. None of these इनमें से कोई नहीं
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D Correct answer
Explanation

For a cylinder: CSA/TSA = 2πrh/(2πrh + 2πr²) = h/(h+r) = 3/5. So 5h = 3h + 3r, giving h = 1.5r. Given CSA = 2πrh = 462, substituting h = 1.5r: 2πr(1.5r) = 462. Using π = 22/7: 2 × (22/7) × 1.5 × r² = 462. Solving: r² = 49, so r = 7 cm and h = 10.5 cm. Volume = πr²h = (22/7) × 49 × 10.5 = 1617 cm³.

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